Answer
$$(s+2)(s^3+2s^2+s-2)=s^4+4s^3+5s^2-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(s+2)(s^3+2s^2+s-2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}s^4+4s^3+5s^2-4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{s+2}\right) $ by each term in $ \left( s^3+2s^2+s-2\right) $. $$ \left( \color{blue}{s+2}\right) \cdot \left( s^3+2s^2+s-2\right) = s^4+2s^3+s^2 -\cancel{2s}+2s^3+4s^2+ \cancel{2s}-4 $$ |
| ② | Combine like terms: $$ s^4+ \color{blue}{2s^3} + \color{red}{s^2} \, \color{green}{ -\cancel{2s}} \,+ \color{blue}{2s^3} + \color{red}{4s^2} + \, \color{green}{ \cancel{2s}} \,-4 = s^4+ \color{blue}{4s^3} + \color{red}{5s^2} -4 $$ |
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